Vehicles may be used in agricultural, forestry, construction, mining, or for other applications. Some applications may require an off-road vehicle to traverse or cover an entire area with one or more paths of the vehicle. For example, a vehicle may be required to plant crops, to harvest crops, or to distribute crop inputs, such as fertilizer or chemicals, over a field or plants within an entire area of a field. If the field has an ordinary rectangular shape, the vehicle operator may cover the entire area of the field by manually or automatically controlling the vehicle to follow an array of parallel sub-paths through the field that are parallel to a linear edge of the field, where a location-determining receiver (e.g., Global Positioning System) receiver may provide location data to assist the operator in following the parallel sub-paths. However, if the field has a complex, irregular polygonal shape, there is a need for automated planning of the path to achieve an efficient solution that minimizes at least one of fuel costs, vehicle operating time, or other operational costs of the vehicle.